SOLUTION: 4^x=3^(x+6) find the solution x=?

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Question 979804: 4^x=3^(x+6)
find the solution
x=?
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
4%5Ex%22%22=%22%223%5E%28x%2B6%29

Take logs of both side:

log%28%284%5Ex%29%29%22%22=%22%22log%28%283%5E%28x%2B6%29%29%29

Move the exponents in front of the logs as factors:

x%2Alog%28%284%29%29%22%22=%22%22%28x%2B6%29log%28%283%29%29

Let log(4) = A and log(3)=B

xA%22%22=%22%22%28x%2B6%29B

Ax%22%22=%22%22B%28x%2B6%29

Ax%22%22=%22%22Bx%2B6B

Ax-Bx%22%22=%22%226B

x%28A-B%29%22%22=%22%226B

x%22%22=%22%22%286B%29%2F%28A-B%29

x%22%22=%22%22%286log%28%283%29%29%29%2F%28log%28%284%29%29-log%28%283%29%29%29

Get your calculator and get:

x%22%22=%22%2222.91305008

Note: you could have used natural logs (ln) as well as common logs (log),
and gotten the same answer.

Edwin